• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Earthquakes and Structures
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• v.26 no.6
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• pp.417-431
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• 2024

The fundamental period of vibration is one of the most critical parameters in the analysis and design of structures, as it depends on the distribution of stiffness and mass within the structure. Therefore, building codes propose empirical equations based on the observed periods of actual buildings during seismic events and ambient vibration tests. However, despite the fact that infill walls increase the stiffness and mass of the structure, causing significant changes in the fundamental period, most of these equations do not account for the presence of infills walls in the structure. Typically, these equations are dependent on both the structural system type and building height. The different values between the empirical and analytical periods are due to the elimination of non-structural effects in the analytical methods. Therefore, the presence of non-structural elements, such as infill panels, should be carefully considered. Another critical factor influencing the fundamental period is the effect of Soil-Structure Interaction (SSI). Most seismic building design codes generally consider SSI to be beneficial to the structural system under seismic loading, as it increases the fundamental period and leads to higher damping of the system. Recent case studies and postseismic observations suggest that SSI can have detrimental effects, and neglecting its impact could lead to unsafe design, especially for structures located on soft soil. The current research focuses on investigating the effect of infill panels on the fundamental period of moment-resisting and eccentrically braced steel frames while considering the influence of soil-structure interaction. To achieve this, the effects of building height, infill wall stiffness, infill openings and soil structure interactions were studied using 3, 6, 9, 12, 15 and 18-story 3-D frames. These frames were modeled and analyzed using SeismoStruct software. The calculated values of the fundamental period were then compared with those obtained from the proposed equation in the seismic code. The results indicate that changing the number of stories and the soil type significantly affects the fundamental period of structures. Moreover, as the percentage of infill openings increases, the fundamental period of the structure increases almost linearly. Additionally, soil-structure interaction strongly affects the fundamental periods of structures, especially for more flexible soils. This effect is more pronounced when the infill wall stiffness is higher. In conclusion, new equations are proposed for predicting the fundamental periods of Moment Resisting Frame (MRF) and Eccentrically Braced Frame (EBF) buildings. These equations are functions of various parameters, including building height, modulus of elasticity, infill wall thickness, infill wall percentage, and soil types.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1237-1248
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• 2009

The domain of attraction of a nonlinear differential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.

• Journal of Korean Society of Steel Construction
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• v.13 no.2
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• pp.163-176
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• 2001

In this paper, the stress resultants and displacements of simply supported curved girder based on the flexural torsional theory considering torsional warping effects are analyzed. And elastic equations of continuous curved girder are obtained by using energy method. Also, bending moment warping torsional moment diagram, pure torsional moment diagram, shearing force diagram, and deflection diagram of continuos curved girder bridge subjecting to vertical loads and uniform loads are presented.

• Steel and Composite Structures
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• v.7 no.2
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• pp.119-133
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• 2007

Based on stability theory of current rigid steel frames and using the three-column subassemblage model, the governing equations for determining the effective length factor (${\mu}$-factor) of the columns in semirigid composite frames are derived. The effects of the nonlinear moment-rotation characteristics of beam-to-column connections and composite action of slab are considered. Furthermore, using a two-bay three-storey composite frame with semi-rigid connections as an example, the effects of the non-linear moment-rotation characteristics of connections and load value on the ${\mu}$-factor are numerically studied and the ${\mu}$-factors obtained by the proposed method and Baraket-Chen's method are compared with those obtained by the exact finite element method. It was found that the proposed method has good accuracy and can be used in stability analysis of semi-rigid composite frames.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.12
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• pp.831-841
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• 2007

This work is to extend the elliptic operator, which has been already adopted in turbulent stress model, to fully developed turbulent buoyant channel flows with changing the orientation of the buoyancy vector to be perpendicular to the channel walls. The turbulent heat flux models based on the elliptic concept are employed and closely linked to the elliptic blending second moment closure which is used for the prediction of Reynolds stresses. In order to reflect the stable or unstable stratification conditions, the present model introduces the gradient Richardson number into the thermal to mechanical time scale ratio and model coefficients. The present model has been applied for the computation of stably and unstably stratified turbulent channel flows and the prediction results are directly compared to the DNS data.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.223-230
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• 1998

The most of the design engineers for construction has academic background of bachelors degree. Theories for advanced composite structures are too difficult for such engineers and some simple but accurate enough methods are necessary. The senior author has reported that some laminate orientations have decreasing values of D$_{16}$, B$_{16}$, D$_{26}$ and B$_{26}$ stiffnesses as the ply number increases. Such plates behave as special orthotropic plates and simple formulas developed by the author can be used. Most of the bridge and building slabs on girders have large aspect ratios. For such cases further simplification is possible by neglecting the effect of the longitudinal moment terms(M$_{x}$) on the relevant partial differential equations of equilibrium. In this paper, the result of the study on the subject problem is presented.ented.d.

• Steel and Composite Structures
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• v.1 no.2
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• pp.213-230
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• 2001

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the nonprismatic properties of a 'cracked' steel-concrete beam. This beam model is extended to a sub-frame in which the restraining effects from the adjoining members are considered. Parametric studies are performed on several sub-frame models and the results are used to show that it is possible to correlate the amount of moment redistribution of semi-continuous beam within the sub-frame using an equivalent stiffness of the connection. Deflection equations are derived for semi-continuous composite beams subjected to various loading and parametric studies on beam vibrations are conducted. The proposed method may be applied using a simple computer or spreadsheet program.

• Wind and Structures
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• v.5 no.5
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• pp.423-440
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• 2002

The effects of the nonlinear (quadratic) term in wind pressure have been analyzed in many papers with reference to linear structural models. The present paper addresses the problem of the response of nonlinear structures to stochastic nonlinear wind pressure. Adopting a single-degree-of-freedom structural model with polynomial nonlinearity, the solution is obtained by means of the moment equation approach in the context of It$\hat{o}$'s stochastic differential calculus. To do so, wind turbulence is idealized as the output of a linear filter excited by a Gaussian white noise. Response statistical moments are computed for both the equivalent linear system and the actual nonlinear one. In the second case, since the moment equations form an infinite hierarchy, a suitable iterative procedure is used to close it. The numerical analyses regard a Duffing oscillator, and the results compare well with Monte Carlo simulation.

• International Journal of Korean Welding Society
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• v.3 no.2
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• pp.7-14
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• 2003

During the manufacture of a ship, longitudinal deformation is produced by fillet welding on the Built­Up beam used to improve the longitudinal strength of a ship. This deformation needs a correcting process separate from a manufacture process and decreases productivity and quality. This deformation is caused by welding moment, which is the value multiplied the shrinking force due to welding by the distance from the neutral axis on a cross section of Built­Up beam. This deformation can be offset by generating a moment which is the same magnitude with and is located in an opposite direction to the welding moment on web plate by induction heating. Accordingly, this study clarifies the creation mechanism of the longitudinal deformation on Built­Up beam with FEM analysis and presents the preventative method of this deformation by induction heating basing the mechanism and verifies its validity through analysis and experiments. The induction heating used here is performed by deciding its location and quantity with experiments and simple equations and by applying them to a real structure.